According to the "feature" cross-reference, all shared hosting plans on GoDaddy (e.g., Economy, Deluxe, Premium) all have the ability to have custom php.ini files along with use of either php5 of php4. So, you should be able to use either. Interestingly, with php5, GoDaddy has globals off by default, whereas on php4, it is not. https://www.godaddy.com/gdshop/hosting/shared.asp?se=&ci=9009#tabs
As for problems, I haven't had any with Joomla, Gallery 2 (Menalto), or SMF on my production site. I have messed with phpBB 3 a bit since SMF and Joomla got a "code divorce" over this whole licensing mess. I haven't had any phpBB issues. In many cases, you will likely have to go to php5 for the next gen versions of any of the major php scripts (Gallery 2 for one). So, I don't really know if there is any reason why it would cause problems unless you had some ancient php scripts. I am sure someone will chime in if I am incorrect since most of what I know was a crash course in the last 9 months.
As for the htaccess file, you should learn the ins and outs, it really is a good tool to help with keeping your site secure. I do not use SEF, so the default settings in the Joomla htaccess are what I am using along with some custom stuff I trial/ errored over time to get to work (e.g., keeping people from leeching graphics, preventing access to key directories, custom error pages)
You definitely want your site to at least have the htaccess items in the Joomla version below the this line:
########## Begin - Rewrite rules to block out some common exploits
You will need the RewriteEngine On declaration as well.
The htaccess entries can do funny things, so you are best to add things slowly, try out, make sure things work. Make sure to turn on the error log in Godaddy control plan to look for errors. GoDaddy pretty much blocks any "php" modification settings in htaccess entries, so you have to be a bit careful when looking at other examples on the Joomla forum but the security forum is a good place to read through for examples of good settings.
Example, in your htaccess file:
# deny access to all .log and .comment files
<Files ~ "^.*\.([Ll][Oo][Gg]|[cC][oO][mM][mM][eE][nN][tT])">
Deny from all
# End deny access to .log and .comment files
That will block someone from reading your log and comment files. Easy to add, and one less thing for someone to use to glean info to hack a site.
#No Directory Listing and Browsing
Options All -Indexes
# End deny directory listing
This set will prevent people from doing a directory listing on your site and cruising around where they shouldn't.
Htaccess settings can get complex depending on what you are trying to do but it is definitely worth getting the basics down (tons of web sites with examples/explanations better than I can give on what all of it means).